At an event held at the stadium, 70% of the audience were adults. The female audience was made up of 30% of the adults and 70% of the children. There were 48 less boys than girls.
- How many people went to the stadium in total?
- Some women left before the event ended, after which 20% of the remaining people at the stadium were women. How many women left the stadium before it ended?
|
Adults |
Children |
Total |
|
7 u |
3 u |
10 u |
|
Women |
Men |
Girls |
Boys |
|
Before |
2.1 u |
4.9 u |
2.1 u |
0.9 u |
|
Change |
- ? |
|
- ? |
After |
|
7.9 u |
|
Comparison in the end |
1 p |
4 p |
5 p |
(a)
70% =
70100 =
710Number of women
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Number of men
= 7 u - 2.1 u
= 4.9 u
Number of girls
= 70% x 3 u
=
70100 x 3 u
= 2.1 u
Number of boys
= 3 u - 2.1 u
= 0.9 u
Number of more girls than boys
= 2.1 u - 0.9 u
= 1.2 u
1.2 u = 48
1 u = 48 ÷ 1.2 = 40
Number of people
= 10 u
= 10 x 40
= 400
(b)
20% =
20100 =
15The total number of men and children in the end is repeated.
7.9 u = 4 p
Number of men and children
= 4.9 u + 3 u
= 7.9 u
= 7.9 x 40
= 316
4 p = 7.9 u
4 p = 316
1 p = 316 ÷ 4 = 79
Number of women in the end
= 1 p
= 79
Number of women at first
= 2.1 u
= 2.1 x 40
= 84
Number of women who left before the event ended
= 84 - 79
= 5
Answers: (a) 400; (b) 5